A line segment is bisected by a line with the equation # 4 y + x = 8 #. If one end of the line segment is at #(5 ,2 )#, where is the other end?

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Answer 1 · 2017-01-03T13:01:34

#B = (75/17, -6/17), AB ⊥ r, |AM| = |MB|#

#A = (5, 2)#

#r: y = 2 - 1/4 x#

#s ⊥ r Rightarrow s : y = a + 4x#

#A in s Rightarrow 2 = a + 4 * 5 Rightarrow a = -18#

#s cap r = M: 2 - 1/4 x = -18 + 4x# // this is cohordinate x of M

#8 - x = -72 + 16x Rightarrow 80 = 17x#

#M = (80/17, 2 - 20/17) = (A + B)/2# // middle point of A and B

#80/17 = (5 + x)/2 and 14/17 = (2 + y)/2# // cohordinates of B

#160 = 85 + 17x and 28 = 34 + 17y#

#75 = 17x and -6 = 17y#